London Algebra Colloquium abstract

Extremely primitive groups

Tim Burness (Southampton), 2nd February 2012

Abstract

A primitive permutation group is said to be extremely primitive if a point stabiliser acts primitively on each of its nontrivial orbits. By a theorem of Mann, Praeger and Seress, every finite extremely primitive group is either almost simple or of affine type, and the affine examples have essentially been classified. I will explain some of the main ideas in the proof of this theorem, and I will report on recent joint work with Cheryl Praeger and Ákos Seress towards a complete classification in the remaining almost simple case.